Summary

David Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlying geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra.

Table of Contents

Preface

vii

To the Instructor

xvii

To the Student

xxiii

Vectors

1

(57)

Introduction: The Racetrack Game

1

(2)

The Geometry and Algebra of Vectors

3

(12)

Length and Angle: The Dot Product

15

(16)

Exploration: Vectors and Geometry

29

(2)

Lines and Planes

31

(16)

Exploration: The Cross Product

45

(2)

Code Vectors and Modular Arithmetic

47

(11)

Vignette: The Codabar System

55

(1)

Chapter Review

56

(2)

Systems of Linear Equations

58

(76)

Introduction: Triviality

58

(1)

Introduction to Systems of Linear Equations

59

(9)

Exploration: Lies My Computer Told Me

66

(2)

Direct Methods for Solving Linear Systems

68

(22)

Exploration: Partial Pivoting

86

(1)

Exploration: Counting Operations: An Introduction to the Analysis of Algorithms